Cluster mean-field approximations with the coherent-anomaly-method analysis for the driven pair contact process with diffusion

Abstract

The cluster mean-field approximations are performed, up to 13 cluster sizes, to study the critical behavior of the driven pair contact process with diffusion (DPCPD) and its precedent, the PCPD in one dimension. Critical points are estimated by extrapolating our data to the infinite cluster size limit, which are in good accordance with recent simulation results. Within the cluster mean-field approximation scheme, the PCPD and the DPCPD share the same mean-field critical behavior. The application of the coherent anomaly method, however, shows that the two models develop different coherent anomalies, which lead to different true critical scaling. The values of the critical exponents for the particle density, the pair density, the correlation length, and the relaxation time are fairly well estimated for the DPCPD. These results support and complement our recent simulation results for the DPCPD.

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Cited by in corpus (13)

• Towards Classification of Phase Transitions in Reaction--Diffusion Models
• Crossover from the pair contact process with diffusion to directed percolation
• Nontrivial critical crossover between directed percolation models: Effect of infinitely many absorbing states
• Critical decay exponent of the pair contact process with diffusion
• Nonequilibrium Phase Transitions into Absorbing States: Focused around the pair contact process with diffusion
• Crossover from the parity-conserving pair contact process with diffusion to other universality classes
• Three different routes from the directed Ising to the directed percolation class
• Monte Carlo simulations of bosonic reaction-diffusion systems
• A coupled two-species model for the pair contact process with diffusion
• Critical Study on the Absorbing Phase Transition in a Four-State Predator-Prey Model in One Dimension
• Generating Function for Particle-Number Probability Distribution in Directed Percolation
• Universality-class crossover by a nonorder field introduced to the pair contact process with diffusion
• Determination of the critical exponents in dissipative phase transitions: Coherent anomaly approach